TSTP Solution File: NUM636^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 08:55:51 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   27 (  11 unt;   4 typ;   0 def)
%            Number of atoms       :   43 (  42 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  145 (  37   ~;  17   |;   2   &;  86   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (  14   ^  26   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    one: $i ).

thf(decl_23,type,
    succ: $i > $i ).

thf(decl_24,type,
    esk1_0: $i ).

thf(decl_25,type,
    esk2_1: ( $i > $o ) > $i ).

thf(satz2,conjecture,
    ! [X1: $i] :
      ( ( succ @ X1 )
     != X1 ),
    file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',satz2) ).

thf(induction,axiom,
    ! [X3: $i > $o] :
      ( ( ( X3 @ one )
        & ! [X1: $i] :
            ( ( X3 @ X1 )
           => ( X3 @ ( succ @ X1 ) ) ) )
     => ! [X2: $i] : ( X3 @ X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',induction) ).

thf(one_is_first,axiom,
    ! [X1: $i] :
      ( ( succ @ X1 )
     != one ),
    file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',one_is_first) ).

thf(succ_injective,axiom,
    ! [X1: $i,X2: $i] :
      ( ( ( succ @ X1 )
        = ( succ @ X2 ) )
     => ( X1 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p',succ_injective) ).

thf(c_0_4,negated_conjecture,
    ~ ! [X1: $i] :
        ( ( succ @ X1 )
       != X1 ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz2])]) ).

thf(c_0_5,plain,
    ! [X15: $i > $o,X17: $i] :
      ( ( ( X15 @ ( esk2_1 @ X15 ) )
        | ~ ( X15 @ one )
        | ( X15 @ X17 ) )
      & ( ~ ( X15 @ ( succ @ ( esk2_1 @ X15 ) ) )
        | ~ ( X15 @ one )
        | ( X15 @ X17 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[induction])])])])])]) ).

thf(c_0_6,negated_conjecture,
    ( ( succ @ esk1_0 )
    = esk1_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

thf(c_0_7,plain,
    ! [X1: $i] :
      ( ( succ @ X1 )
     != one ),
    inference(fof_simplification,[status(thm)],[one_is_first]) ).

thf(c_0_8,plain,
    ! [X1: $i,X3: $i > $o] :
      ( ( X3 @ X1 )
      | ~ ( X3 @ ( succ @ ( esk2_1 @ X3 ) ) )
      | ~ ( X3 @ one ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,negated_conjecture,
    ( ( succ @ esk1_0 )
    = esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,plain,
    ! [X12: $i] :
      ( ( succ @ X12 )
     != one ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).

thf(c_0_11,plain,
    ! [X1: $i] :
      ( ( X1
       != ( succ @ X1 ) )
      | ( one
        = ( succ @ one ) )
      | ( ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) )
        = ( succ
          @ ( succ
            @ ( esk2_1
              @ ^ [Z0: $i] :
                  ( Z0
                 != ( succ @ Z0 ) ) ) ) ) ) ),
    inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_8,c_0_9]) ).

thf(c_0_12,plain,
    ! [X1: $i] :
      ( ( succ @ X1 )
     != one ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_13,plain,
    ! [X1: $i,X3: $i > $o] :
      ( ( X3 @ ( esk2_1 @ X3 ) )
      | ( X3 @ X1 )
      | ~ ( X3 @ one ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_14,plain,
    ! [X13: $i,X14: $i] :
      ( ( ( succ @ X13 )
       != ( succ @ X14 ) )
      | ( X13 = X14 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[succ_injective])])]) ).

thf(c_0_15,plain,
    ! [X1: $i] :
      ( ( ( succ
          @ ( succ
            @ ( esk2_1
              @ ^ [Z0: $i] :
                  ( Z0
                 != ( succ @ Z0 ) ) ) ) )
        = ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) ) )
      | ( ( succ @ X1 )
       != X1 ) ),
    inference(sr,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_16,plain,
    ! [X1: $i] :
      ( ( X1
       != ( succ @ X1 ) )
      | ( ( esk2_1
          @ ^ [Z0: $i] :
              ( Z0
             != ( succ @ Z0 ) ) )
       != ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) ) )
      | ( one
        = ( succ @ one ) ) ),
    inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13,c_0_9]) ).

thf(c_0_17,plain,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ( ( succ @ X1 )
       != ( succ @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_18,negated_conjecture,
    ( ( succ
      @ ( succ
        @ ( esk2_1
          @ ^ [Z0: $i] :
              ( Z0
             != ( succ @ Z0 ) ) ) ) )
    = ( succ
      @ ( esk2_1
        @ ^ [Z0: $i] :
            ( Z0
           != ( succ @ Z0 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_9]) ).

thf(c_0_19,plain,
    ! [X1: $i] :
      ( ( ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) )
       != ( esk2_1
          @ ^ [Z0: $i] :
              ( Z0
             != ( succ @ Z0 ) ) ) )
      | ( ( succ @ X1 )
       != X1 ) ),
    inference(sr,[status(thm)],[c_0_16,c_0_12]) ).

thf(c_0_20,negated_conjecture,
    ! [X1: $i] :
      ( ( ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) )
        = X1 )
      | ( ( succ
          @ ( esk2_1
            @ ^ [Z0: $i] :
                ( Z0
               != ( succ @ Z0 ) ) ) )
       != ( succ @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_21,negated_conjecture,
    ( ( succ
      @ ( esk2_1
        @ ^ [Z0: $i] :
            ( Z0
           != ( succ @ Z0 ) ) ) )
   != ( esk2_1
      @ ^ [Z0: $i] :
          ( Z0
         != ( succ @ Z0 ) ) ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_9]) ).

thf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% 0.08/0.10  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n025.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Fri May  3 09:30:13 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  Running higher-order theorem proving
% 0.14/0.39  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.THmzNkqd3c/E---3.1_32334.p
% 0.14/0.40  # Version: 3.1.0-ho
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40  # Starting full_lambda_8 with 300s (1) cores
% 0.14/0.40  # Starting new_ho_13 with 300s (1) cores
% 0.14/0.40  # Starting ho_unfolding_3 with 300s (1) cores
% 0.14/0.40  # new_ho_14 with pid 32412 completed with status 0
% 0.14/0.40  # Result found by new_ho_14
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.40  # Search class: HGUSF-FFSF11-DSFFFSBN
% 0.14/0.40  # partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.14/0.40  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.40  # Starting new_ho_14 with 901s (1) cores
% 0.14/0.40  # Starting new_ho_13 with 151s (1) cores
% 0.14/0.40  # Starting ho_unfolding_6 with 151s (1) cores
% 0.14/0.40  # Starting sh4l with 151s (1) cores
% 0.14/0.40  # Starting full_lambda_8 with 146s (1) cores
% 0.14/0.40  # new_ho_13 with pid 32417 completed with status 0
% 0.14/0.40  # Result found by new_ho_13
% 0.14/0.40  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.14/0.40  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.40  # Starting new_ho_14 with 1500s (5) cores
% 0.14/0.40  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.40  # Search class: HGUSF-FFSF11-DSFFFSBN
% 0.14/0.40  # partial match(1): HGUSF-FFSF11-SSFFFSBN
% 0.14/0.40  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.40  # Starting new_ho_14 with 901s (1) cores
% 0.14/0.40  # Starting new_ho_13 with 151s (1) cores
% 0.14/0.40  # Preprocessing time       : 0.001 s
% 0.14/0.40  # Presaturation interreduction done
% 0.14/0.40  
% 0.14/0.40  # Proof found!
% 0.14/0.40  # SZS status Theorem
% 0.14/0.40  # SZS output start CNFRefutation
% See solution above
% 0.14/0.40  # Parsed axioms                        : 6
% 0.14/0.40  # Removed by relevancy pruning/SinE    : 2
% 0.14/0.40  # Initial clauses                      : 5
% 0.14/0.40  # Removed in clause preprocessing      : 0
% 0.14/0.40  # Initial clauses in saturation        : 9
% 0.14/0.40  # Processed clauses                    : 25
% 0.14/0.40  # ...of these trivial                  : 0
% 0.14/0.40  # ...subsumed                          : 2
% 0.14/0.40  # ...remaining for further processing  : 23
% 0.14/0.40  # Other redundant clauses eliminated   : 0
% 0.14/0.40  # Clauses deleted for lack of memory   : 0
% 0.14/0.40  # Backward-subsumed                    : 2
% 0.14/0.40  # Backward-rewritten                   : 1
% 0.14/0.40  # Generated clauses                    : 12
% 0.14/0.40  # ...of the previous two non-redundant : 9
% 0.14/0.40  # ...aggressively subsumed             : 0
% 0.14/0.40  # Contextual simplify-reflections      : 0
% 0.14/0.40  # Paramodulations                      : 10
% 0.14/0.40  # Factorizations                       : 0
% 0.14/0.40  # NegExts                              : 0
% 0.14/0.40  # Equation resolutions                 : 2
% 0.14/0.40  # Disequality decompositions           : 0
% 0.14/0.40  # Total rewrite steps                  : 1
% 0.14/0.40  # ...of those cached                   : 0
% 0.14/0.40  # Propositional unsat checks           : 0
% 0.14/0.40  #    Propositional check models        : 0
% 0.14/0.40  #    Propositional check unsatisfiable : 0
% 0.14/0.40  #    Propositional clauses             : 0
% 0.14/0.40  #    Propositional clauses after purity: 0
% 0.14/0.40  #    Propositional unsat core size     : 0
% 0.14/0.40  #    Propositional preprocessing time  : 0.000
% 0.14/0.40  #    Propositional encoding time       : 0.000
% 0.14/0.40  #    Propositional solver time         : 0.000
% 0.14/0.40  #    Success case prop preproc time    : 0.000
% 0.14/0.40  #    Success case prop encoding time   : 0.000
% 0.14/0.40  #    Success case prop solver time     : 0.000
% 0.14/0.40  # Current number of processed clauses  : 11
% 0.14/0.40  #    Positive orientable unit clauses  : 2
% 0.14/0.40  #    Positive unorientable unit clauses: 0
% 0.14/0.40  #    Negative unit clauses             : 4
% 0.14/0.40  #    Non-unit-clauses                  : 5
% 0.14/0.40  # Current number of unprocessed clauses: 2
% 0.14/0.40  # ...number of literals in the above   : 4
% 0.14/0.40  # Current number of archived formulas  : 0
% 0.14/0.40  # Current number of archived clauses   : 13
% 0.14/0.40  # Clause-clause subsumption calls (NU) : 14
% 0.14/0.40  # Rec. Clause-clause subsumption calls : 14
% 0.14/0.40  # Non-unit clause-clause subsumptions  : 1
% 0.14/0.40  # Unit Clause-clause subsumption calls : 4
% 0.14/0.40  # Rewrite failures with RHS unbound    : 0
% 0.14/0.40  # BW rewrite match attempts            : 1
% 0.14/0.40  # BW rewrite match successes           : 1
% 0.14/0.40  # Condensation attempts                : 0
% 0.14/0.40  # Condensation successes               : 0
% 0.14/0.40  # Termbank termtop insertions          : 959
% 0.14/0.40  # Search garbage collected termcells   : 116
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.004 s
% 0.14/0.40  # System time              : 0.001 s
% 0.14/0.40  # Total time               : 0.005 s
% 0.14/0.40  # Maximum resident set size: 1860 pages
% 0.14/0.40  
% 0.14/0.40  # -------------------------------------------------
% 0.14/0.40  # User time                : 0.011 s
% 0.14/0.40  # System time              : 0.007 s
% 0.14/0.40  # Total time               : 0.018 s
% 0.14/0.40  # Maximum resident set size: 1708 pages
% 0.14/0.40  % E---3.1 exiting
% 0.14/0.40  % E exiting
%------------------------------------------------------------------------------